Flash Distillation Material Balance
We are given a continuous flash distillation scenario involving components A and B. Key parameters are:
- Feed Rate ($F$): $100$ kmol/h
- Feed Composition (Equimolar): Mole fraction of A, $x_F = 0.5$
- Liquid Product Composition: Mole fraction of A, $x_L = 0.4$
- Relative Volatility ($\alpha_{AB}$): $6$
The goal is to determine the vapor product rate ($V$) in kmol/h.
Equilibrium Vapor Composition
The first step is to find the mole fraction of A in the vapor phase ($y_V$) that is in equilibrium with the liquid phase composition ($x_L = 0.4$). We use the formula derived from relative volatility:
$ y_V = \frac{\alpha \cdot x_L}{1 + (\alpha - 1) \cdot x_L} $
Substituting the given values:
$ y_V = \frac{6 \times 0.4}{1 + (6 - 1) \times 0.4} = \frac{2.4}{1 + (5 \times 0.4)} = \frac{2.4}{1 + 2.0} = \frac{2.4}{3.0} = 0.8 $
Thus, the vapor product has a mole fraction of A ($y_V$) equal to $0.8$ (or $80\%$).
Solving for Vapor Product Rate
We apply the principle of conservation of mass. Let $L$ be the liquid product rate.
1. Total Material Balance:
$ F = L + V $ $ 100 = L + V \implies L = 100 - V $ 2. Component A Material Balance: $ F \cdot x_F = L \cdot x_L + V \cdot y_V $ 3. Substitute $L$ and known values into the Component A Balance: $ 100 \times 0.5 = (100 - V) \times 0.4 + V \times 0.8 $ $ 50 = (100 \times 0.4) - (V \times 0.4) + (V \times 0.8) $ $ 50 = 40 - 0.4V + 0.8V $ $ 50 - 40 = (0.8 - 0.4)V $ $ 10 = 0.4V $ 4. Calculate $V$: $ V = \frac{10}{0.4} = \frac{100}{4} $ $ V = 25 \text{ kmol/h} $Final Answer
The vapor product rate is $25$ kmol/h.
Important Questions from Distillation
A binary mixture of butane and butadiene is to be separated in an extractive distillation using furfural. Furfural lowers the activity of butadiene more than it does for butane. Consider the distillation sequence shown in the figure.
Match the component labels in Group I with chemical species in Group II.
Group I Group II P. Component X 1. Butane Q. Component Y 2. Butadiene R. Component Z 3. Furfural A continuous distillation column is used to separate an equimolar mixture of diethylamine (DEA) and methanol. The feed enters the column as saturated liquid at a flow rate of $30 \text{ mol s}^{-1}$. It is desired to obtain $92 \text{ mol}\%$ DEA as distillate. The rate of withdrawal of the distillate from the column is $10 \text{ mol s}^{-1}$. The equilibrium curve for the conditions in the column is given below. The latent heat of vaporization of the reboiler contents is $35 \text{ kJ mol}^{-1}$. Neglect heat loss to the surroundings and assume constant molal overflow. Which one of the following is the minimum reboiler heat duty (in kW)?
- A binary AB liquid mixture containing 30 mol% A is subjected to differential (Rayleigh) distillation at atmospheric pressure in order to recover 60 mol% A in the distillate. Assuming a constant relative volatility $ \alpha_{AB} = 2.2 $, the average composition of the collected distillate is _______ mol% A (rounded off to nearest integer).
- Identify the WRONG statement amongst the following:
A binary feed consisting of $25$ mol% liquid and $75$ mol% vapour is separated in a staged distillation column. The mole fraction of the more volatile component in the distillate product is $0.95$. The molar flow rate of distillate is $50$% of the feed flow rate and the McCabe-Thiele method can be used to analyze the column. The q-line intersects the operating line of the enriching section at $(0.35, 0.5)$ on the x-y diagram. The slope of the stripping section operating line (up to one decimal place) is ____________
